Abstract In this work, a model on the interaction dynamics of mosquitoes causing vector-borne diseases is formulated, without consider the human population as dynamic variables and including mobility from eulerian approach, in which the populations are not assigned to a place in particular, but they move between patches at certain rates. The results suggest that in order to eradicate the disease, the mosquito population in each patch must be controlled, but in order to reduce the magnitude of an epidemic outbreak, the transformation rate from susceptible to infected, the migration and immigration rate must be controlled.